"Non-computable" refers to problems or functions that cannot be solved or calculated by any algorithm or computer. This means there is no step-by-step procedure that can be followed to arrive at a solution, regardless of the amount of time or resources available. An example of a non-computable problem is the Halting Problem, which determines whether a given program will finish running or continue indefinitely. In the realm of mathematics and computer science, non-computable functions highlight the limitations of computation. While many problems can be solved using algorithms, non-computable ones demonstrate that there are inherent boundaries to what can be achieved through mechanical processes. This concept is crucial for understanding the limits of Turing machines and the nature of computability theory.